# Factors, Multiples and Primes - Short Problems

### Weekly Problem 10 - 2008

##### Stage: 3 and 4 Challenge Level:

If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

### Weekly Problem 14 - 2008

##### Stage: 3 and 4 Challenge Level:

The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?

### Weekly Problem 22 - 2008

##### Stage: 3 and 4 Challenge Level:

The following sequence continues indefinitely... Which of these integers is a multiple of 81?

### Weekly Problem 26 - 2008

##### Stage: 3 and 4 Challenge Level:

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

### Weekly Problem 41 - 2008

##### Stage: 3 Challenge Level:

How many pairs of numbers of the form x, 2x+1 are there in which both numbers are prime numbers less than 100?

### Weekly Problem 1 - 2009

##### Stage: 3 Short Challenge Level:

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

### Weekly Problem 11 - 2009

##### Stage: 3 Short Challenge Level:

How many of the numbers 1 to 20 are not the sum of two primes?

### Weekly Problem 13 - 2009

##### Stage: 3 Short Challenge Level:

How many zeros does 50! have at the end?

### Weekly Problem 41 - 2009

##### Stage: 2 and 3 Short Challenge Level:

At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. How much did is cost this group of adults and children to see a film?

### Weekly Problem 45 - 2009

##### Stage: 2 and 3 Short Challenge Level:

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

### Weekly Problem 6 - 2010

##### Stage: 2 and 3 Short Challenge Level:

Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

### Weekly Problem 7 - 2010

##### Stage: 3 Short Challenge Level:

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

### Weekly Problem 22 - 2010

##### Stage: 3 Short Challenge Level:

Can you form this 2010-digit number...

### Weekly Problem 30 - 2010

##### Stage: 3 and 4 Short Challenge Level:

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

### Weekly Problem 48 - 2010

##### Stage: 3 Short Challenge Level:

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

### Weekly Problem 5 - 2011

##### Stage: 3 and 4 Short Challenge Level:

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

### Weekly Problem 7 - 2011

##### Stage: 3 and 4 Short Challenge Level:

Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

### Weekly Problem 10 - 2011

##### Stage: 3 and 4 Short Challenge Level:

Will this product give a perfect square?

### Weekly Problem 25 - 2011

##### Stage: 2 and 3 Short Challenge Level:

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

### Weekly Problem 5 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 5 - 2014

### Weekly Problem 15 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 15 - 2014

### Weekly Problem 26 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 26 - 2014

### Weekly Problem 28 - 2014

##### Stage: 4 Challenge Level:

Weekly Problem 28 - 2014

### Weekly Problem 39 - 2014

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 39 - 2014

### Weekly Problem 1 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 1 - 2015

### Weekly Problem 4 - 2015

##### Stage: 3 and 4 Challenge Level:

Weekly Problem 4 - 2015

### Weekly Problem 1 - 2016

##### Stage: 3 Short Challenge Level:

What is the last-but-one digit of 99! ?

### Weekly Problem 2 - 2016

##### Stage: 3 Short Challenge Level:

How many tables of each type does Mark need at his birthday party?

### Weekly Problem 3 - 2016

##### Short Challenge Level:

How many times has Simon's age changed from a square to a prime?

### Weekly Problem 7 - 2016

##### Stage: 3 Short Challenge Level:

What is the smallest number of pieces grandma should cut her cake into to guarentee each grandchild gets the same amount of cake and none is left over.

### Weekly Problem 18 - 2016

##### Stage: 3 and 4 Short Challenge Level:

The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?

### Weekly Problem 25 - 2016

##### Stage: 3 Short Challenge Level:

A list is made of every digit that is the units digit of at least one prime number. How many digits appear in the list?

### Weekly Problem 28 - 2016

##### Stage: 3 Short Challenge Level:

Last week, Tom and Sophie bought some stamps for their collections. Each stamp Tom bought cost him £1.10, whilst Sophie paid 70p for each of her stamps. Between them they spent exactly £10. How many stamps did they buy in total?

### Weekly Problem 36 - 2016

##### Stage: 3 and 4 Short Challenge Level:

What percentage of the integers between 1 and 10,000 are square numbers?

### Weekly Problem 38 - 2016

##### Stage: 3 and 4 Short Challenge Level:

To power should 4^4 be raised to give 8^8?